Question

derive the formula of compound interest! ​

Answer 1

compound interest = Amount - Principle.

hope it will help you.

Answer 2

QUESTION:-

✯ᴅᴇʀɪᴠᴇ ᴛʜᴇ ғᴏʀᴍᴜʟᴀ ᴏғ ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇsᴛ!

SOLUTION ✔

✯DERIVATION,

✯ᴅᴇʀɪᴠɪɴɢ, ᴄᴏᴍᴘᴏᴜɴᴅ ɪɴᴛᴇʀᴇsᴛ ғᴏʀᴍᴜʟᴀ,

LET,

$\sf\therefore principal\:amount\:=p$

$\sf\therefore time= n\:years$

$\sf\therefore rate =R$

$\sf\large\therefore simple \:interest\:for\:firsr\:year,$

$\sf\therefore SI_1= \dfrac{P \times R \times T }{100}$

$\sf\therefore amount\:after\:1_st \:year=p+SI_1$

$\sf\implies P+ \dfrac{P times R \times T }{100}$

$\sf\therefore P \times \bigg( 1+ \dfrac{R}{100} \bigg)=P_2$

$\sf\therefore simple\:intrest\:for\:2_nd \:= \dfrac{P_2 \times R \times T }{100}$

$\sf\therefore Amount\:after\:second\:year,$

$\sf\implies P_2 +SI_2$

$\sf\implies P_2+ \dfrac{P_2 \times R \times T }{100}$

$\sf\implies P_2 \bigg( 1+ \dfrac{R}{100} \bigg)$

$\sf\implies P \bigg( 1+ \dfrac{R}{100} \bigg) \times \bigg( 1+ \dfrac{R}{100} \bigg)$

$\sf\therefore P \bigg( 1+ \dfrac{R}{100} \bigg)^2$

$\sf\therefore simlarly\:if\:we\:continued,\:for\:"n"\:years.$

THEN,

$\sf\therefore A=P \times \bigg( 1+ \dfrac{R}{100} \bigg)^n$

$\sf\large\therefore CI=A-P$

$\sf\implies p \times \bigg[ \bigg( 1+ \dfrac{R}{100} \bigg)^n \bigg]$

$\sf{\boxed{\sf{ \therefore p \times \bigg[ \bigg( 1+ \dfrac{R}{100} \bigg)^n \bigg]}}}$